So, for a "Treachery"-style Weakness, it has some sort of Revelation effect. The rules state to treat it like it was drawn from the threat deck.
After the Revelation is done, does the card...
1. Get discarded to the player's discard; or 2. Get discarded to the threat deck's discard; or 3. Stick around in your hand to gum it up.
(1) is the intuitive answer. (2) seems to be the literal rules, but raises more questions. (3) is a possibility the rules state that you cannot discard Weaknesses (though I think that means discarding instead of playing).